As possible answer to the following message of Tobias Schroeder to this list
all introductions to field and Galois theory I've found are written in a "classical" way, i.e. making not much use of categorical notions. A lot of computation is done where someone who is "categorical minded" has the feeling that the results could be established in a more comprehensible and clear way by category theory. -- Does somebody have a reference to a short and good introduction to field and Galois theory from a categorical viewpoint?
let me mention the book Galois theories Francis Borceux & George Janelidze Cambridge Studies in Advanced Mathematics, volume 72 Cambridge University Press (2001), 341 pages ISBN 0 521 80309 8 which will be available from February 20. This is probably not an as "short" introduction as Tobias wants ... and I let you decide if it is a "good" one. References at the end of the book, in particular to various papers of George Janelidze on a categorical approach of Galois theory, will provide alternative answers to Tobias'question. Here is the table of contents of the book. 1. Classical Galois theory 2. Galois theory of Grothendieck 3. Infinitary Galois theory 4. Categorical Galois theory of commutative rings 5. Categorical Galois theorem and factorization systems 6. Covering maps 7. Non-galoisian Galois theory For further information, contact WWW: http://www.cambridge.org Francis Borceux %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Francis Borceux doyen de la faculté des Sciences, Université Catholique de Louvain 2 place des Sciences, 1348 Louvain-la-neuve (Belgique) tél. 32 10 473170 fax 32 10 472837 secrétaire 32 10 478679